Question 1: What is 5ED4 – 07A4 when these values represent signed 16-bit hexadecimal numbers stored in sign-magnitude format? The result should be written in hexadecimal. Show your work.
Question 2: What is 4365 – 3412 when these values represent signed 12- bit octal numbers stored in sign-magnitude format. The result should be written in octal. Show your work.
Question 3: Assume 185 and 122 are signed 8-bit decimal integers stored in sign-magnitude format. Calculate 185 – 122. Is there overflow, underflow, or neither?
Question 4: Assume 151 and 214 are signed 8-bit decimal integers stored in two’s complement format. Calculate 151 – 214 saturating arithmetic. The result should be written in decimal. Show your work.
Question 5: Write down the binary representation of the decimal number 63.25 assuming the IEEE 754 single precision format.
Question 6: Calculate the sum of 2.6125 X 101 and 4.150390625 X 10-1 by hand, assuming A and B are stored in the 16-bit half precision described in exercise 3.27. Assume 1 guard, 1 round bit, and 1 sticky bit, and round to the nearest even. Show all steps.
/* REFERENCE PURPOSES ONLY Exercise 3.27:
IEEE 754-2008 contains a half precision that is only 16 bits wide. The leftmost bit is still the sign bit, the exponent is 5 bits wide and has a bias of 15 and the mantissa is 10 bits long. A hidden 1 is assumed.
*/
Question 7: Write down the bit pattern in the fraction of value 1/3 assuming a floating point format that uses binary numbers in the fraction. Assume there are 24 bits, and you do not need to normalize. Is this representation exact?
